Method for determining a physical parameter of a compressible medium with a measuring transducer of vibration-type and measuring transducer for performing such a method

Abstract

A method for determining density and/or mass flow of a compressible medium with a measuring transducer of vibration-type having at least two oscillators, each including a pair of measuring tubes, wherein the pairs of measuring tubes are arranged for parallel flow, wherein the two oscillators have mutually independent oscillator oscillations with mutually differing eigenfrequencies for corresponding oscillation modes. The method includes steps of determining the values of the eigenfrequencies of at least two different oscillator oscillations, determining at least two preliminary density measured values based on the values of the eigenfrequencies, and determining a correction term for one of the preliminary density measured values and/or for a preliminary measured value of flow based on the preliminary density measured values and the values of the eigenfrequencies.

The invention claimed is: 
     
       1. A method for determining a physical parameter of a compressible medium using a measuring transducer of vibration-type, the method comprising:
 providing a measuring transducer of vibration-type having at least two oscillators, each oscillator including a pair of measuring tubes, wherein the pairs of measuring tubes are arranged for parallel flow, and wherein the at least two oscillators have mutually independent oscillator oscillations with mutually differing eigenfrequencies for corresponding oscillation modes; 
 determining the values of the eigenfrequencies of at least two different oscillator oscillations; 
 determining at least two preliminary density measured values based on the values of the eigenfrequencies; and 
 determining a correction term for one of the preliminary density measured values, and/or for a preliminary measured value of flow, based on the preliminary density measured values and the values of the eigenfrequencies. 
 
     
     
       2. The method of  claim 1 , wherein the correction term for a preliminary density measured value of an oscillator depends on the value of the eigenfrequency of the oscillator and on either a quotient between the velocity of sound in the medium, which contains microbubbles therein, or a resonance frequency of oscillations of the microbubble-containing medium relative to a measuring tube of the oscillator. 
     
     
       3. The method of  claim 1 , wherein the eigenfrequencies of a same bending oscillation mode of the at least two oscillators are ascertained and used for determining the correction term. 
     
     
       4. The method of  claim 1 , wherein the eigenfrequency of a wanted mode and the eigenfrequency of an f3 mode are ascertained and used for determining the correction term. 
     
     
       5. The method of  claim 4 , wherein the lowest available eigenfrequency of the wanted mode is used for determining the correction term. 
     
     
       6. The method of  claim 4 , wherein the highest available eigenfrequency of the f3 mode is used for determining the correction term. 
     
     
       7. The method of  claim 1 , wherein the correction term for the preliminary density measured value based on the eigenfrequency of a selected oscillation mode has the form: 
       
         
           
             
               
                 
                   K 
                   
                     i 
                     , 
                     j 
                   
                 
                 := 
                 
                   ( 
                   
                     1 
                     + 
                     
                       r 
                       
                         
                           
                             ( 
                             
                               
                                 g 
                                 · 
                                 c 
                               
                               
                                 f 
                                 
                                   i 
                                   , 
                                   j 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         - 
                         b 
                       
                     
                   
                   ) 
                 
               
               , 
               
                 
 
               
               ⁢ 
               
                 
                   wherein 
                   : 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       ρ 
                       corr 
                     
                     · 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       i 
                       , 
                       j 
                     
                   
                   
                     K 
                     
                       i 
                       , 
                       j 
                     
                   
                 
               
               , 
             
           
         
         wherein index i refers to the selected mode, and index j refers to a selected oscillator of the at least two oscillators, and 
         wherein K i,j  is the correction term, ρ i,j  is the preliminary density measured value, r and g are media independent constants, c is the velocity of sound in the medium, f i,j  is the eigenfrequency of the selected mode, ρ corr  is the corrected density, and b is a scaling constant, wherein a ratio r/b<1 and/or b=1. 
       
     
     
       8. The method of  claim 7 , wherein the ratio r/b<0.9 and/or b=1. 
     
     
       9. The method of  claim 7 , wherein a density error of a preliminary density value based on the eigenfrequency of the selected mode is:
     E   ρi,j   :=K   i,j −1,
 
 
       wherein E ρi,j  is the density error, and
 wherein a mass flow error of a preliminary mass flow value through the measuring tube pair of the selected oscillator with the index j is ascertained proportionally to the density error of the first preliminary density value based on the eigenfrequency of the selected oscillator in the f1 mode, thus:
     E   m,j   :=k·E   ρ1,j , 
 
 
       wherein E m,j  is the mass flow error E m,j , the proportionality factor k is not less than 1.5 and not more than 3. 
     
     
       10. The method of  claim 9 , wherein the proportionality factor kin not less than 1.8 and not more than 2.25. 
     
     
       11. The method of  claim 9 , wherein the proportionality factor k is 2. 
     
     
       12. The method as claimed in  claim 9 , wherein a correction term for the mass flow value is ascertained as:
     K   m,j :=1+ E   m,j , 
 
       wherein K m  is the correction term for the mass flow value, and a corrected mass flow through the measuring tube pair of the oscillator with the index j is ascertained as: 
       
         
           
             
               
                 
                   
                     
                       m 
                       . 
                     
                     
                       corr 
                       , 
                       j 
                     
                   
                   · 
                 
                 = 
                 
                   
                     
                       m 
                       . 
                     
                     
                       v 
                       , 
                       j 
                     
                   
                   
                     K 
                     
                       m 
                       , 
                       j 
                     
                   
                 
               
               , 
             
           
         
       
       wherein {dot over (m)} corr,j  is the corrected mass flow, and {dot over (m)} v,j  is the preliminary mass flow value through the measuring tube pair of the oscillator with the index j, and
 wherein a total corrected mass flow through the measuring transducer is ascertained by summing the contributions of the at least two oscillators, thus:
     {dot over (m)}   corr,total   ={dot over (m)}   corr,1   +{dot over (m)}   corr,2 , 
 
 
       wherein {dot over (m)} corr,total  is the total corrected mass flow. 
     
     
       13. A measuring transducer of vibration-type for determining a physical parameter of a compressible medium, comprising:
 first, second, third and fourth measuring tubes, each having an inlet end and an outlet end, wherein all inlet ends and all outlet ends of the measuring tubes are combined with respective collectors at each end for parallel flow; 
 a first actuator arrangement and a second actuator arrangement; 
 a first sensor arrangement and a second sensor arrangement, each configured to register oscillations and generate signals based thereon; and 
 an operating and processing circuit configured to drive the first and second actuator arrangements and to register the signals of the first and second sensor arrangements, 
 wherein the first measuring tube and the second measuring tube are connected at or near their inlet ends with a first rigid node plate and at or near their outlet ends with a second rigid node plate, the first and second node plates arranged spaced from each respective collector at its respective end to form a first oscillator, wherein the first actuator arrangement is adapted to excite a wanted mode between the two measuring tubes of the first oscillator, 
 wherein the third measuring tube and the fourth measuring tube are connected at or near their inlet ends with a third rigid node plate and at or near their outlet ends with a fourth rigid node plate, the third and fourth node plates arranged spaced from each respective collector at its respective end to form a second oscillator, wherein the second actuator arrangement is adapted to excite a wanted mode between the two measuring tubes of the second oscillator, 
 wherein the first oscillator and the second oscillator each have at least one wanted mode with first and second wanted mode eigenfrequencies, respectively, 
 wherein the magnitude of the difference between the wanted mode eigenfrequencies of the two oscillators is at least 0.1 times the lesser of the first and second wanted mode eigenfrequencies, 
 wherein the first sensor arrangement is adapted to register oscillations of the first oscillator, and the second sensor arrangement is adapted to register oscillations of the second oscillator, 
 wherein the operating circuit and evaluating circuit is configured to drive the first and second actuator arrangements such that bending oscillation modes of the first and second oscillators are excited at at least the eigenfrequencies of the wanted modes independently of one another, and 
 wherein the operating and evaluating circuit is further configured to: 
 determining the values of the eigenfrequencies of at least two different oscillator oscillations; 
 determining at least two preliminary density measured values based on the values of the eigenfrequencies; and 
 determining a correction term for one of the preliminary density measured values, and/or for a preliminary measured value of flow, based on the preliminary density measured values and the values of the eigenfrequencies. 
 
     
     
       14. The measuring transducer of  claim 13 , wherein the magnitude of the difference between the wanted mode eigenfrequencies of the two oscillators is at least 0.4 times the lesser of the two wanted mode eigenfrequencies. 
     
     
       15. The measuring transducer of  claim 13 , wherein the first and second measuring tubes of the first oscillator extend symmetrically relative to a first mirror plane, which extends between the measuring tubes of the first oscillator, and wherein the third and fourth measuring tubes of the second oscillator extend symmetrically relative to the first mirror plane, which further extends between the measuring tubes of the second oscillator. 
     
     
       16. The measuring transducer of  claim 15 , wherein the first and second measuring tubes of the first oscillator extend symmetrically relative to a second mirror plane, which extends perpendicularly to the first mirror plane and intersects the measuring tubes of the first oscillator, wherein the third and fourth measuring tubes of the second oscillator extend symmetrically relative to the second mirror plane and are intersected by the second mirror plane, and wherein the measuring tubes oscillate in the wanted mode perpendicularly to the first mirror plane and symmetrically to the second mirror plane. 
     
     
       17. The measuring transducer of  claim 13 , wherein the operating and evaluating circuit is further configured to drive the first and second actuator arrangements such that the wanted modes of the first and second oscillators are excited simultaneously. 
     
     
       18. The measuring transducer of  claim 16 , wherein the measuring tubes of at least one oscillator are excited in a second oscillatory mode symmetric to the second mirror plane and having a higher eigenfrequency than the wanted mode of the at least one oscillator. 
     
     
       19. The measuring transducer of  claim 18 , wherein the operating and evaluating circuit is further configured to drive the first and second actuator arrangements such that at least one f3 mode is excited simultaneously with the wanted mode of the at least one oscillator or with the wanted modes of both oscillators.